Chapter 22: Ratio, Proportion and Proof
Ratios are used to compare quantities
You can find equivalent ratios by multiplying or dividing by the same number
To write a ratio in its simplest form, find an equivalent ratio with the smallest possible whole number values
If you use x to represent one part of the ratio, then you can write the length of the x as x
Then form an equation and solve it to find x
If the ratio contains decimals or fractions-multiply
If the ratio has mixed units-convert to the smaller unit
Two quantities are in direct proportion when both quantities increase at the same rate
Two quantities are in inverse proportion when one quantity increases at the same rate as the other quantity decreases
You can use common sense to work out whether to divide or multiply in proportion questions
6 people build a wall in 4 days
6x4=24 so 1 person could build the wall in 24 days
24/8=3 so 8 people could build the wall in 3 days
Show your method by writing down what you are working out at each stage of your working
Read the question carefully-you have to write down the option which offers better value
You won’t get the final mark if you just circle or underline your choice
You can use algebra to prove facts about numbers
Using algebra helps you to probe that something is true for every number
In a proof question the working is the answer
If the question say ‘show that’ or ‘prove that’ you need to write down every stage of your working
If you don’t you won’t get all the marks
If you need to prove something about numbers then you always use algebra
Even number = 2n
Odd number = 2n+1 or 2n-1
Multiple of 3 = 3n
Consecutive numbers = n,n+1.n+2…
Consecutive even numbers = 2n,2n+2,2n+4…
Consecutive odd numbers = 2n+1,2n+3,2n+5…
Ratios are used to compare quantities
You can find equivalent ratios by multiplying or dividing by the same number
To write a ratio in its simplest form, find an equivalent ratio with the smallest possible whole number values
If you use x to represent one part of the ratio, then you can write the length of the x as x
Then form an equation and solve it to find x
If the ratio contains decimals or fractions-multiply
If the ratio has mixed units-convert to the smaller unit
Two quantities are in direct proportion when both quantities increase at the same rate
Two quantities are in inverse proportion when one quantity increases at the same rate as the other quantity decreases
You can use common sense to work out whether to divide or multiply in proportion questions
6 people build a wall in 4 days
6x4=24 so 1 person could build the wall in 24 days
24/8=3 so 8 people could build the wall in 3 days
Show your method by writing down what you are working out at each stage of your working
Read the question carefully-you have to write down the option which offers better value
You won’t get the final mark if you just circle or underline your choice
You can use algebra to prove facts about numbers
Using algebra helps you to probe that something is true for every number
In a proof question the working is the answer
If the question say ‘show that’ or ‘prove that’ you need to write down every stage of your working
If you don’t you won’t get all the marks
If you need to prove something about numbers then you always use algebra
Even number = 2n
Odd number = 2n+1 or 2n-1
Multiple of 3 = 3n
Consecutive numbers = n,n+1.n+2…
Consecutive even numbers = 2n,2n+2,2n+4…
Consecutive odd numbers = 2n+1,2n+3,2n+5…
